Dark Matter Halos: The Dynamical Basis of Effective Empirical Models

TL;DR

This paper links empirical galaxy density models to underlying dynamical solutions, providing a physical basis for commonly used profiles and a way to evaluate small-scale dynamical effects.

Contribution

It establishes -profiles as the dynamical foundation for empirical models like Sersic-Einasto and generalized NFW, bridging theory and observation.

Findings

Empirical models closely approximate dynamical solutions.

Parameters of empirical models can be derived from dynamical models.

Provides a baseline for assessing small-scale dynamical effects.

Abstract

We investigate the dynamical basis of the classic empirical models (specifically, Sersic-Einasto and generalized NFW) that are widely used to describe the distributions of collisionless matter in galaxies. We submit that such a basis is provided by our \alpha-profiles, shown to constitute solutions of the Jeans dynamical equilibrium with physical boundary conditions. We show how to set the parameters of the empirical in terms of the dynamical models; we find the empirical models, and specifically Sersic-Einasto, to constitute a simple and close approximation to the dynamical models. Finally, we discuss how these provide an useful baseline for assessing the impact of the small-scale dynamics that may modulate the density slope in the central galaxy regions.